PSI - Issue 57

Boris Spak et al. / Procedia Structural Integrity 57 (2024) 445–451 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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coefficient of friction. The sheet materialis modelled with the assumption of isotropic hardening, using materialcard *MAT_03 with an underlying cost efficient bilinear stress strain curve. The plastic hardening parameter β is set to unity, with an average Young’s modulus E = 62.7 GPa, ν = 0.33, yield stress R p02 = 400 MPa and tangent modulus E TAN = 700 MPa, respectively. Fig. 2 right shows the sheet dimensions, the definition of the local coordinate system used to prescribe displacement and rotation of both rolls as well as a close up the chosen meshing with linear solid hexahedron elements within the expected region of high degree of forming. To obtain a sufficient number of elements through sheet thickness, two separate convergence studies had been performed beforehand. The number of elements through thickness varied between six and 24 with a uniform element edge length: a simple bending simulation in 2D to keep the computing costs low, as well as a loading simulation in 3D under bending and torsion with an angled sheet. The results obtained showed that quadrupling the number of elements from six to 24 yields a change of 8 % in the highly stressed area, quantified in terms of the equivalent stress σ eqv . A further modification to five elements showed no significant changes and was regarded as an acceptable compromise between accuracy and computation time. Thinking ahead, a simple strip was embedded in the middle of the sheet material. This strip will be used in the loading simulation to carry out the fatigue life estimation with the Local Strain Approach. Three different tool paths were chosen to study the impact of the forming operation on the residual stress distribution in the strip and the effect on the estimated fatigue life, as shown in fig. 3. In tool path variant 1, the rolls are rotated linearly by 10 ° each time they are displaced in the positive direction of the local axis z r . While returning, the angle remains unchanged.Variant 2 sees a linear increase in the rotation of the rolls by 10 ° each time it passes along the sheet material. Lastly, in variant 3 the rolls are rotated by 10 ° within a small displacement increment along the local axis z r each time the rolls pass along the sheet material. The totalrotation of the rolls is set

Fig. 3. Different tool path variants and distribution of residual stresses in the formed strip in terms of the equivalent stress σ eqv .

to reach 90 ° at the end of the process simulation for all variants with the aim to achieve a similar angled geometry. The embedded strip is cut from the surrounding sheet material to be subjected to different cyclic loading regimes. Fig. 3 presents the residual stress in terms of the equivalent stress σ eqv for each tool path variant in the inner radius of the formed strip. By comparing the results in each strip, the residual stress distribution varies in distribution as well as in the magnitude, with variant 3 showing the highest values in σ eqv . 3. Fatigue life estimation under different loading conditions The LSA is a frequently used concept to estimate fatigue life of notched components. Based on solid research over several decades, the concept has proven its overall applicability for notched components Radaj & Vormwald (2007), spot welds Radaj et al. (2006), mechanical joints Spak et al. (2022) and was introduced as the German FKM Guidelin e nonlinear (FKM nonlinear, 2019) to industrial users. Being a so-called material-based concept, the fatigue life estimation is assumed to be applicable to different geometries as long as the cyclic material properties are known. Extension exist to consider residual stresses, as discussed in Kühne et al. (2021) as well as transient cyclic material behavior by Kühne et al. (2019). The material properties can be obtained either through estimation methods based on